In internal combustion engines, a fuel cut is executed where a predetermined condition is fulfilled. The fuel cut is the processing of stopping the supply of fuel to the internal combustion engine. For example, the fuel cut is executed during deceleration. Further, where oxygen is supplied to a catalyst provided in the exhaust passage of the internal combustion engine when the catalyst temperature is high, thermal degradation of the catalyst advances. A method is known by which the fuel cut is prohibited so that no oxygen is supplied to the catalyst when the catalyst temperature is equal to or higher than a predetermined temperature (see, for example, Patent Literature 1).
In addition to the catalyst, a filter that traps particulate matter (referred to hereinbelow as PM) contained in exhaust gas can be also provided in the exhaust passage of an internal combustion engine. Where the PM amount trapped in the filter reaches a certain level, the processing of oxidizing and removing the PM is executed. This processing is filter regeneration. In order to oxidize the PM trapped in the filter, the filter temperature needs to be equal to or higher than a predetermined temperature and the concentration of oxygen in the filter needs to be equal to or higher than a predetermined concentration.
Meanwhile, the usual gasoline engine normally operates at a stoichiometric or rich air-fuel ratio. Therefore, there are few cases in which the oxygen concentration inside the filter becomes equal to or higher than the predetermined concentration, and such an event is limited, for example, to a fuel cut period. However, as disclosed in Patent Literature 1, where thermal degradation of the catalyst is to be suppressed, oxygen cannot be supplied to the filter. Therefore, the filter is difficult to regenerate. Even in a lean-burn gasoline engine, operation is sometimes executed at a stoichiometric or rich air-fuel ratio, and the filter can therefore be difficult to regenerate.